NPB Model for Birth Weight
Sheena Martenies
02/10/2021
#' -----------------------------------------------------------------------------
#' Install the new version of the package
#' -----------------------------------------------------------------------------
#library(devtools)
#install_github("lvhoskovec/mmpack", build_vignettes = TRUE, force = TRUE)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.3 ✓ purrr 0.3.4
## ✓ tibble 3.0.6 ✓ dplyr 1.0.4
## ✓ tidyr 1.1.2 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.5.0## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(lubridate)##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, unionlibrary(haven)
library(readxl)
library(mmpack)
#' For ggplots
simple_theme <- theme(
#aspect.ratio = 1,
text = element_text(family="Calibri",size = 12, color = 'black'),
panel.spacing.y = unit(0,"cm"),
panel.spacing.x = unit(0.25, "lines"),
panel.grid.minor = element_line(color = "transparent"),
panel.grid.major = element_line(color = "transparent"),
panel.border=element_rect(fill = NA),
panel.background=element_blank(),
axis.ticks = element_line(colour = "black"),
axis.text = element_text(color = "black", size=10),
# legend.position = c(0.1,0.1),
plot.margin=grid::unit(c(0,0,0,0), "mm"),
legend.key = element_blank()
)
# windowsFonts(Calibri=windowsFont("TT Calibri"))
options(scipen = 9999) #avoid scientific notation
set.seed(123)1 Sensitivty Analysis
In this version of the analysis, we are stratifying by race/ethnicity. This is the script for NHW participants. 05_NPB_Model_BW_v4c.Rmd has the script for all non-NHW participants
1.1 Exposure data
#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, mean_temp, pct_tree_cover, pct_impervious,
mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
as.matrix()
head(X)## mean_pm mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 7.454146 48.57052 58.01924 17.205991 31.67281
## [2,] 6.671239 50.06429 61.35590 6.842898 45.00359
## [3,] 6.952053 47.03291 57.13183 9.468662 44.01263
## [4,] 7.071838 46.19062 57.04334 4.563177 65.57617
## [5,] 7.104422 50.67264 59.19456 1.230547 13.83406
## [6,] 7.262078 47.48769 57.41438 8.196283 30.41568
## mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,] 9048.6468 3350.3033 2992.2968 5211.871
## [2,] 4223.3434 3364.9542 6998.1286 8921.318
## [3,] 10552.9404 3132.8384 3075.6670 5396.864
## [4,] 15609.0030 546.6841 701.0141 3137.313
## [5,] 758.5468 6983.3297 1408.5728 3985.479
## [6,] 10775.8211 2227.6615 617.1256 4116.912
## dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,] 7423.232 36079.21 4887.2996 221.0414 157.6974
## [2,] 9636.816 42235.78 3752.6399 203.8812 142.5368
## [3,] 3903.573 38311.68 5829.9603 204.8360 164.1012
## [4,] 4540.787 42527.04 1408.5747 315.0113 223.5397
## [5,] 3660.698 18821.69 368.4558 233.5437 184.0995
## [6,] 4164.256 36113.37 2984.1470 341.3953 244.7493
## violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,] 7.636888 46.78194 6.891702 4.564963
## [2,] 2.850212 21.95270 2.725915 5.623583
## [3,] 7.521877 53.88196 8.581395 9.193457
## [4,] 26.089340 99.75336 48.019560 12.475378
## [5,] 8.924274 58.29613 1.166329 3.401797
## [6,] 17.700302 57.79417 8.269720 5.705853
## pct_limited_eng pct_hh_pov pct_poc
## [1,] 0.0000000 6.307978 26.63305
## [2,] 1.3506213 9.292274 32.68648
## [3,] 2.9942418 11.516315 36.17576
## [4,] 27.6394850 29.098712 85.33845
## [5,] 0.9844560 0.880829 30.93407
## [6,] 0.8856089 11.512915 57.82769Variance and histograms of the exposure variables (in their original units):
var(X)## mean_pm mean_o3 mean_temp
## mean_pm 0.37533486393 -0.00009847023 0.14642749
## mean_o3 -0.00009847023 8.90678204139 10.81282268
## mean_temp 0.14642749300 10.81282267988 19.23803359
## pct_tree_cover -0.31562039249 -0.49673758943 0.26736627
## pct_impervious 0.38998516298 -3.36196169567 3.38371752
## mean_aadt_intensity -40.76212708884 571.26841631737 3039.21948584
## dist_m_tri -228.65604957972 840.63416900145 -1142.86850331
## dist_m_npl -327.26389334167 389.22033402881 -1214.35656220
## dist_m_waste_site -293.39148494029 195.76264386557 -505.75477845
## dist_m_major_emit 75.38286752654 367.90099165114 -601.13695742
## dist_m_cafo -1799.04879699667 -113.10061840529 -1295.48918289
## dist_m_mine_well -438.58618797980 -470.07420537707 -698.86208401
## cvd_rate_adj 5.15458179100 -1.76990043482 8.96033736
## res_rate_adj 2.87311588429 0.02209233438 10.86044869
## violent_crime_rate 0.37556375702 0.09420255053 1.16980254
## property_crime_rate 3.74337501727 -6.32086264144 5.99654104
## pct_less_hs 1.11407811657 0.08820859257 1.16622766
## pct_unemp 0.09672587993 -0.14200322662 -0.26389936
## pct_limited_eng 0.46489777874 0.01861635300 -0.06416471
## pct_hh_pov 0.63511223840 -2.17346396822 -0.43383702
## pct_poc 1.86865059261 -0.72243796509 -1.30303053
## pct_tree_cover pct_impervious mean_aadt_intensity
## mean_pm -0.3156204 0.3899852 -40.76213
## mean_o3 -0.4967376 -3.3619617 571.26842
## mean_temp 0.2673663 3.3837175 3039.21949
## pct_tree_cover 14.1689558 12.3764189 12952.91511
## pct_impervious 12.3764189 225.0431814 72329.23445
## mean_aadt_intensity 12952.9151084 72329.2344546 76732213.59795
## dist_m_tri -1379.0480931 -22311.2104303 -4067115.32674
## dist_m_npl -667.9200776 -16864.1211853 -3109131.62176
## dist_m_waste_site 2439.0858422 -4500.5284810 1286423.15512
## dist_m_major_emit -436.0804870 -3795.1383553 -1041488.63725
## dist_m_cafo 13600.2783324 27181.7544247 19866500.22215
## dist_m_mine_well 4340.8882115 5061.5932972 4025007.15834
## cvd_rate_adj -35.3818150 247.5995298 12773.47708
## res_rate_adj -5.7237056 206.6624054 41562.89919
## violent_crime_rate -7.0628378 34.8268766 5586.24923
## property_crime_rate -41.0349096 215.2833687 32259.22575
## pct_less_hs -7.7049973 36.5523244 -513.17767
## pct_unemp 0.4702494 16.7021455 6155.35866
## pct_limited_eng -2.1021233 26.7336819 6276.00173
## pct_hh_pov 3.3644024 71.6622471 23153.87384
## pct_poc -21.2173929 45.7892837 -6097.13108
## dist_m_tri dist_m_npl dist_m_waste_site
## mean_pm -228.6560 -327.2639 -293.39148
## mean_o3 840.6342 389.2203 195.76264
## mean_temp -1142.8685 -1214.3566 -505.75478
## pct_tree_cover -1379.0481 -667.9201 2439.08584
## pct_impervious -22311.2104 -16864.1212 -4500.52848
## mean_aadt_intensity -4067115.3267 -3109131.6218 1286423.15512
## dist_m_tri 8490021.8257 5223807.4506 2383742.58458
## dist_m_npl 5223807.4506 12187017.8728 4352248.88385
## dist_m_waste_site 2383742.5846 4352248.8838 5182882.45939
## dist_m_major_emit 2128915.6157 7565465.0730 2146855.37143
## dist_m_cafo 1596357.7408 3577908.2118 5528792.90409
## dist_m_mine_well 508901.5232 450437.9950 1628102.57019
## cvd_rate_adj -54234.0707 -50226.3231 -39856.32468
## res_rate_adj -37463.4960 -37762.5969 -30012.13465
## violent_crime_rate -1294.7171 -2173.8745 -4931.44436
## property_crime_rate -14980.2601 -37647.1447 -34802.06130
## pct_less_hs -8358.4384 -1944.7470 -5770.15391
## pct_unemp -1346.7988 2331.6340 55.46268
## pct_limited_eng -3297.6197 2069.4486 -649.93969
## pct_hh_pov -7541.4611 -2577.2448 -3859.50474
## pct_poc -11784.0293 2897.7440 -1796.48889
## dist_m_major_emit dist_m_cafo dist_m_mine_well
## mean_pm 75.38287 -1799.0488 -438.5862
## mean_o3 367.90099 -113.1006 -470.0742
## mean_temp -601.13696 -1295.4892 -698.8621
## pct_tree_cover -436.08049 13600.2783 4340.8882
## pct_impervious -3795.13836 27181.7544 5061.5933
## mean_aadt_intensity -1041488.63725 19866500.2222 4025007.1583
## dist_m_tri 2128915.61570 1596357.7408 508901.5232
## dist_m_npl 7565465.07295 3577908.2118 450437.9950
## dist_m_waste_site 2146855.37143 5528792.9041 1628102.5702
## dist_m_major_emit 10618148.39450 -5198964.4718 -1562078.1806
## dist_m_cafo -5198964.47181 59322312.4584 11831250.8310
## dist_m_mine_well -1562078.18063 11831250.8310 4934706.5090
## cvd_rate_adj -6735.51280 -63409.9471 -39314.7418
## res_rate_adj -18729.44986 -31915.1779 -18578.9530
## violent_crime_rate -3279.14786 -218.4570 -2296.2682
## property_crime_rate -37357.36924 -39512.2233 -10770.1549
## pct_less_hs 6683.56459 -20906.1580 -8122.5732
## pct_unemp 3863.27118 360.2569 -1459.2637
## pct_limited_eng 6147.89974 -2449.5928 -3366.9959
## pct_hh_pov 3537.17769 3206.6101 -2618.1959
## pct_poc 17131.22545 -37400.8490 -19965.8349
## cvd_rate_adj res_rate_adj violent_crime_rate
## mean_pm 5.154582 2.87311588 0.37556376
## mean_o3 -1.769900 0.02209233 0.09420255
## mean_temp 8.960337 10.86044869 1.16980254
## pct_tree_cover -35.381815 -5.72370563 -7.06283776
## pct_impervious 247.599530 206.66240537 34.82687661
## mean_aadt_intensity 12773.477081 41562.89918523 5586.24922880
## dist_m_tri -54234.070749 -37463.49600671 -1294.71708456
## dist_m_npl -50226.323102 -37762.59685160 -2173.87453741
## dist_m_waste_site -39856.324678 -30012.13464859 -4931.44436485
## dist_m_major_emit -6735.512802 -18729.44985583 -3279.14786226
## dist_m_cafo -63409.947058 -31915.17788201 -218.45697058
## dist_m_mine_well -39314.741764 -18578.95304228 -2296.26822650
## cvd_rate_adj 2191.182815 1385.29494365 150.70808516
## res_rate_adj 1385.294944 1156.71343313 121.65371220
## violent_crime_rate 150.708085 121.65371220 53.66783212
## property_crime_rate 566.337526 472.63650773 256.55496614
## pct_less_hs 231.479433 145.54238485 16.54740871
## pct_unemp 67.363344 51.69113046 9.04149094
## pct_limited_eng 110.257122 67.33790262 9.28416690
## pct_hh_pov 181.657547 152.91320652 25.02326808
## pct_poc 494.097173 253.35297277 39.91113843
## property_crime_rate pct_less_hs pct_unemp
## mean_pm 3.743375 1.11407812 0.09672588
## mean_o3 -6.320863 0.08820859 -0.14200323
## mean_temp 5.996541 1.16622766 -0.26389936
## pct_tree_cover -41.034910 -7.70499732 0.47024939
## pct_impervious 215.283369 36.55232441 16.70214553
## mean_aadt_intensity 32259.225754 -513.17766924 6155.35865920
## dist_m_tri -14980.260099 -8358.43835664 -1346.79876430
## dist_m_npl -37647.144722 -1944.74702528 2331.63404217
## dist_m_waste_site -34802.061301 -5770.15391068 55.46268468
## dist_m_major_emit -37357.369240 6683.56458897 3863.27117705
## dist_m_cafo -39512.223334 -20906.15798373 360.25692941
## dist_m_mine_well -10770.154916 -8122.57321486 -1459.26372738
## cvd_rate_adj 566.337526 231.47943304 67.36334415
## res_rate_adj 472.636508 145.54238485 51.69113046
## violent_crime_rate 256.554966 16.54740871 9.04149094
## property_crime_rate 2092.599784 2.37207933 -4.44996391
## pct_less_hs 2.372079 100.97051611 24.75412746
## pct_unemp -4.449964 24.75412746 16.99668272
## pct_limited_eng -10.993591 45.55561336 14.53021864
## pct_hh_pov 85.141940 53.74957643 22.28487081
## pct_poc -32.166948 167.47523501 53.90073829
## pct_limited_eng pct_hh_pov pct_poc
## mean_pm 0.46489778 0.6351122 1.868651
## mean_o3 0.01861635 -2.1734640 -0.722438
## mean_temp -0.06416471 -0.4338370 -1.303031
## pct_tree_cover -2.10212332 3.3644024 -21.217393
## pct_impervious 26.73368187 71.6622471 45.789284
## mean_aadt_intensity 6276.00173099 23153.8738357 -6097.131081
## dist_m_tri -3297.61965954 -7541.4610842 -11784.029327
## dist_m_npl 2069.44857387 -2577.2447547 2897.744008
## dist_m_waste_site -649.93968840 -3859.5047430 -1796.488891
## dist_m_major_emit 6147.89973970 3537.1776917 17131.225451
## dist_m_cafo -2449.59276096 3206.6101083 -37400.848996
## dist_m_mine_well -3366.99587133 -2618.1959480 -19965.834924
## cvd_rate_adj 110.25712151 181.6575467 494.097173
## res_rate_adj 67.33790262 152.9132065 253.352973
## violent_crime_rate 9.28416690 25.0232681 39.911138
## property_crime_rate -10.99359078 85.1419396 -32.166948
## pct_less_hs 45.55561336 53.7495764 167.475235
## pct_unemp 14.53021864 22.2848708 53.900738
## pct_limited_eng 35.59148773 34.6946706 90.364663
## pct_hh_pov 34.69467062 75.9843174 96.120981
## pct_poc 90.36466320 96.1209811 431.057094ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Scaling the exposure variables
X.scaled <- apply(X, 2, scale)
head(X.scaled)## mean_pm mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] -0.04466117 0.2557710 1.258916 2.8650572 -0.4317392
## [2,] -1.32257091 0.7562940 2.019647 0.1119669 0.4568939
## [3,] -0.86420910 -0.2594409 1.056593 0.8095353 0.3908364
## [4,] -0.66868869 -0.5416715 1.036418 -0.4936707 1.8282681
## [5,] -0.61550307 0.9601351 1.526878 -1.3790272 -1.6208750
## [6,] -0.35816558 -0.1070584 1.121012 0.4715111 -0.5155396
## mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,] -0.09084216 -0.2344047 -0.6085424 0.03971116
## [2,] -0.64169521 -0.2293766 0.5389346 1.66909525
## [3,] 0.08088689 -0.3090384 -0.5846609 0.12096980
## [4,] 0.65808323 -1.1966032 -1.2648840 -0.87154355
## [5,] -1.03723382 1.0124451 -1.0622027 -0.49898458
## [6,] 0.10633078 -0.6196939 -1.2889140 -0.44125230
## dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,] -0.02150275 -0.1312893 0.5115705609 -0.21472100 -0.02194817
## [2,] 0.65781307 0.6680473 0.0007893036 -0.58131344 -0.46770979
## [3,] -1.10163310 0.1585630 0.9359211172 -0.56091550 0.16634114
## [4,] -0.90608162 0.7058640 -1.0544209929 1.79274970 1.91399256
## [5,] -1.17616773 -2.3719154 -1.5226435621 0.05236468 0.75434311
## [6,] -1.02163351 -0.1268541 -0.3451574045 2.35639005 2.53761051
## violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,] -0.5964233 -0.258738271 -0.4702609 -0.8122686
## [2,] -1.2498200 -0.801513939 -0.8848327 -0.5554906
## [3,] -0.6121227 -0.103529459 -0.3021056 0.3104157
## [4,] 1.9223962 0.899234905 3.6227114 1.1064759
## [5,] -0.4206909 -0.007034139 -1.0400400 -1.0944053
## [6,] 0.7772654 -0.018007256 -0.3331230 -0.5355351
## pct_limited_eng pct_hh_pov pct_poc
## [1,] -0.8611272 -0.63784322 -0.8362933
## [2,] -0.6347355 -0.29548558 -0.5447291
## [3,] -0.3592312 -0.04034434 -0.3766674
## [4,] 3.7718149 1.97670312 1.9912592
## [5,] -0.6961123 -1.26044411 -0.6291337
## [6,] -0.7126811 -0.04073434 0.6662003Variance and histograms of the exposure variables (scaled):
var(X.scaled)## mean_pm mean_o3 mean_temp pct_tree_cover
## mean_pm 1.00000000000 -0.00005385612 0.054492011 -0.13686320
## mean_o3 -0.00005385612 1.00000000000 0.826034772 -0.04421786
## mean_temp 0.05449201081 0.82603477185 1.000000000 0.01619412
## pct_tree_cover -0.13686319671 -0.04421785696 0.016194120 1.00000000
## pct_impervious 0.04243319193 -0.07509299382 0.051425773 0.21917608
## mean_aadt_intensity -0.00759553767 0.02185198723 0.079102983 0.39283460
## dist_m_tri -0.12809106580 0.09667011226 -0.089425530 -0.12573497
## dist_m_npl -0.15301708182 0.03735823800 -0.079308030 -0.05082845
## dist_m_waste_site -0.21035477359 0.02881268488 -0.050649362 0.28462463
## dist_m_major_emit 0.03776059293 0.03783085448 -0.042059944 -0.03555276
## dist_m_cafo -0.38126281823 -0.00492034473 -0.038348150 0.46910476
## dist_m_mine_well -0.32226625571 -0.07090475229 -0.071726638 0.51913345
## cvd_rate_adj 0.17973997428 -0.01266919781 0.043642007 -0.20080378
## res_rate_adj 0.13788937407 0.00021765483 0.072803882 -0.04470905
## violent_crime_rate 0.08367913752 0.00430868974 0.036406187 -0.25612577
## property_crime_rate 0.13357057516 -0.04629913234 0.029886660 -0.23830956
## pct_less_hs 0.18097096497 0.00294139393 0.026460967 -0.20370715
## pct_unemp 0.03829580051 -0.01154132622 -0.014594053 0.03030241
## pct_limited_eng 0.12719643719 0.00104558928 -0.002452126 -0.09360870
## pct_hh_pov 0.11892661145 -0.08354684403 -0.011347084 0.10253616
## pct_poc 0.14690996353 -0.01165930732 -0.014308920 -0.27149116
## pct_impervious mean_aadt_intensity dist_m_tri dist_m_npl
## mean_pm 0.04243319 -0.007595538 -0.12809107 -0.15301708
## mean_o3 -0.07509299 0.021851987 0.09667011 0.03735824
## mean_temp 0.05142577 0.079102983 -0.08942553 -0.07930803
## pct_tree_cover 0.21917608 0.392834601 -0.12573497 -0.05082845
## pct_impervious 1.00000000 0.550417300 -0.51042954 -0.32201942
## mean_aadt_intensity 0.55041730 1.000000000 -0.15934675 -0.10167204
## dist_m_tri -0.51042954 -0.159346754 1.00000000 0.51355154
## dist_m_npl -0.32201942 -0.101672036 0.51355154 1.00000000
## dist_m_waste_site -0.13177860 0.064507365 0.35935134 0.54762002
## dist_m_major_emit -0.07763728 -0.036487262 0.22422274 0.66506258
## dist_m_cafo 0.23525319 0.294458074 0.07113229 0.13306733
## dist_m_mine_well 0.15188807 0.206846001 0.07862283 0.05808388
## cvd_rate_adj 0.35259616 0.031151643 -0.39762941 -0.30735717
## res_rate_adj 0.40505655 0.139509596 -0.37804283 -0.31805354
## violent_crime_rate 0.31690170 0.087051131 -0.06065456 -0.08500192
## property_crime_rate 0.31371441 0.080504839 -0.11238850 -0.23574377
## pct_less_hs 0.24248495 -0.005830175 -0.28547853 -0.05543922
## pct_unemp 0.27005813 0.170444274 -0.11211565 0.16200543
## pct_limited_eng 0.29871207 0.120093947 -0.18970252 0.09936486
## pct_hh_pov 0.54801887 0.303230454 -0.29691976 -0.08469250
## pct_poc 0.14701563 -0.033525037 -0.19479240 0.03998010
## dist_m_waste_site dist_m_major_emit dist_m_cafo
## mean_pm -0.21035477 0.03776059 -0.381262818
## mean_o3 0.02881268 0.03783085 -0.004920345
## mean_temp -0.05064936 -0.04205994 -0.038348150
## pct_tree_cover 0.28462463 -0.03555276 0.469104758
## pct_impervious -0.13177860 -0.07763728 0.235253189
## mean_aadt_intensity 0.06450737 -0.03648726 0.294458074
## dist_m_tri 0.35935134 0.22422274 0.071132289
## dist_m_npl 0.54762002 0.66506258 0.133067328
## dist_m_waste_site 1.00000000 0.28939613 0.315308448
## dist_m_major_emit 0.28939613 1.00000000 -0.207149275
## dist_m_cafo 0.31530845 -0.20714928 1.000000000
## dist_m_mine_well 0.32193294 -0.21579814 0.691498053
## cvd_rate_adj -0.37400057 -0.04415775 -0.175877000
## res_rate_adj -0.38761298 -0.16900040 -0.121835919
## violent_crime_rate -0.29568646 -0.13736610 -0.003871683
## property_crime_rate -0.33417673 -0.25061600 -0.112144852
## pct_less_hs -0.25223447 0.20412043 -0.270126943
## pct_unemp 0.00590926 0.28757340 0.011345437
## pct_limited_eng -0.04785357 0.31624911 -0.053310381
## pct_hh_pov -0.19448402 0.12452900 0.047761190
## pct_poc -0.03800769 0.25321920 -0.233886431
## dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm -0.32226626 0.17973997 0.1378893741
## mean_o3 -0.07090475 -0.01266920 0.0002176548
## mean_temp -0.07172664 0.04364201 0.0728038823
## pct_tree_cover 0.51913345 -0.20080378 -0.0447090537
## pct_impervious 0.15188807 0.35259616 0.4050565514
## mean_aadt_intensity 0.20684600 0.03115164 0.1395095959
## dist_m_tri 0.07862283 -0.39762941 -0.3780428333
## dist_m_npl 0.05808388 -0.30735717 -0.3180535435
## dist_m_waste_site 0.32193294 -0.37400057 -0.3876129844
## dist_m_major_emit -0.21579814 -0.04415775 -0.1690004014
## dist_m_cafo 0.69149805 -0.17587700 -0.1218359191
## dist_m_mine_well 1.00000000 -0.37808153 -0.2459108457
## cvd_rate_adj -0.37808153 1.00000000 0.8701418420
## res_rate_adj -0.24591085 0.87014184 1.0000000000
## violent_crime_rate -0.14110257 0.43948112 0.4882648378
## property_crime_rate -0.10598593 0.26448007 0.3037884703
## pct_less_hs -0.36388628 0.49212544 0.4258722177
## pct_unemp -0.15933862 0.34906174 0.3686557880
## pct_limited_eng -0.25406149 0.39481557 0.3318743018
## pct_hh_pov -0.13521021 0.44519692 0.5157866800
## pct_poc -0.43290182 0.50840014 0.3587944499
## violent_crime_rate property_crime_rate pct_less_hs
## mean_pm 0.083679138 0.133570575 0.180970965
## mean_o3 0.004308690 -0.046299132 0.002941394
## mean_temp 0.036406187 0.029886660 0.026460967
## pct_tree_cover -0.256125773 -0.238309563 -0.203707154
## pct_impervious 0.316901702 0.313714407 0.242484946
## mean_aadt_intensity 0.087051131 0.080504839 -0.005830175
## dist_m_tri -0.060654559 -0.112388497 -0.285478530
## dist_m_npl -0.085001918 -0.235743774 -0.055439219
## dist_m_waste_site -0.295686456 -0.334176726 -0.252234466
## dist_m_major_emit -0.137366103 -0.250616004 0.204120426
## dist_m_cafo -0.003871683 -0.112144852 -0.270126943
## dist_m_mine_well -0.141102571 -0.105985926 -0.363886281
## cvd_rate_adj 0.439481116 0.264480066 0.492125439
## res_rate_adj 0.488264838 0.303788470 0.425872218
## violent_crime_rate 1.000000000 0.765561899 0.224789323
## property_crime_rate 0.765561899 1.000000000 0.005160465
## pct_less_hs 0.224789323 0.005160465 1.000000000
## pct_unemp 0.299364943 -0.023595616 0.597541745
## pct_limited_eng 0.212428529 -0.040283149 0.759926412
## pct_hh_pov 0.391854663 0.213519954 0.613642986
## pct_poc 0.262403541 -0.033868765 0.802760342
## pct_unemp pct_limited_eng pct_hh_pov pct_poc
## mean_pm 0.03829580 0.127196437 0.11892661 0.14690996
## mean_o3 -0.01154133 0.001045589 -0.08354684 -0.01165931
## mean_temp -0.01459405 -0.002452126 -0.01134708 -0.01430892
## pct_tree_cover 0.03030241 -0.093608696 0.10253616 -0.27149116
## pct_impervious 0.27005813 0.298712073 0.54801887 0.14701563
## mean_aadt_intensity 0.17044427 0.120093947 0.30323045 -0.03352504
## dist_m_tri -0.11211565 -0.189702515 -0.29691976 -0.19479240
## dist_m_npl 0.16200543 0.099364864 -0.08469250 0.03998010
## dist_m_waste_site 0.00590926 -0.047853566 -0.19448402 -0.03800769
## dist_m_major_emit 0.28757340 0.316249109 0.12452900 0.25321920
## dist_m_cafo 0.01134544 -0.053310381 0.04776119 -0.23388643
## dist_m_mine_well -0.15933862 -0.254061495 -0.13521021 -0.43290182
## cvd_rate_adj 0.34906174 0.394815571 0.44519692 0.50840014
## res_rate_adj 0.36865579 0.331874302 0.51578668 0.35879445
## violent_crime_rate 0.29936494 0.212428529 0.39185466 0.26240354
## property_crime_rate -0.02359562 -0.040283149 0.21351995 -0.03386877
## pct_less_hs 0.59754175 0.759926412 0.61364299 0.80276034
## pct_unemp 1.00000000 0.590768043 0.62010617 0.62971673
## pct_limited_eng 0.59076804 1.000000000 0.66715649 0.72955521
## pct_hh_pov 0.62010617 0.667156489 1.00000000 0.53111530
## pct_poc 0.62971673 0.729555212 0.53111530 1.00000000ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.2 Covariate data
Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.
W <- select(hs_data2,
lat, lon, lat_lon_int,
ed_no_hs, ed_hs, ed_aa, ed_4yr,
low_bmi, ovwt_bmi, obese_bmi,
concep_spring, concep_summer, concep_fall,
concep_2010, concep_2011, concep_2012, concep_2013,
maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
male, gest_age_w) %>%
as.matrix()
head(W)## lat lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,] 39.74934 -104.9129 -4170.219 0 0 0 0 0
## [2,] 39.68397 -104.8933 -4162.583 0 0 1 0 0
## [3,] 39.77109 -105.0477 -4177.861 0 0 0 1 0
## [4,] 39.71579 -105.0205 -4170.971 0 1 0 0 0
## [5,] 39.88283 -104.7784 -4178.860 0 0 1 0 0
## [6,] 39.75980 -104.9562 -4173.037 0 0 0 0 0
## ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,] 0 0 0 0 0 1
## [2,] 0 0 1 0 0 1
## [3,] 0 0 0 0 0 1
## [4,] 0 1 1 0 0 1
## [5,] 0 0 1 0 0 1
## [6,] 0 0 0 0 0 1
## concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,] 0 0 0 34 0 0
## [2,] 0 0 0 28 0 0
## [3,] 0 0 0 33 0 0
## [4,] 0 0 0 31 0 0
## [5,] 0 0 0 31 0 0
## [6,] 0 0 0 36 1 0
## mean_cpss mean_epsd male gest_age_w
## [1,] 19 1 0 40.42857
## [2,] 20 0 0 36.28571
## [3,] 22 4 1 41.57143
## [4,] 17 0 1 41.00000
## [5,] 23 9 0 38.57143
## [6,] 21 5 0 40.57143Scaled the non-binary (continuous) covariates
colnames(W)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male" "gest_age_w"W.s <- apply(W[,c(1, 2, 3, 18, 21, 22, 24)], 2, scale) #' just the continuous ones
W.scaled <- cbind(W.s[,1:3],
W[,4:17], W.s[,4],
W[,19:20], W.s[,5:6],
W[,23], W.s[,7])
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "" ""colnames(W.scaled) <- colnames(W)
head(W.scaled)## lat lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,] 0.2674191 -0.4798892 -0.4051852 0 0 0 0 0
## [2,] -0.5948425 -0.2716453 0.3840107 0 0 1 0 0
## [3,] 0.5542857 -1.9109032 -1.1949511 0 0 0 1 0
## [4,] -0.1750665 -1.6218003 -0.4829104 0 1 0 0 0
## [5,] 2.0281845 0.9480022 -1.2981784 0 0 1 0 0
## [6,] 0.4054444 -0.9392257 -0.6964047 0 0 0 0 0
## ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,] 0 0 0 0 0 1
## [2,] 0 0 1 0 0 1
## [3,] 0 0 0 0 0 1
## [4,] 0 1 1 0 0 1
## [5,] 0 0 1 0 0 1
## [6,] 0 0 0 0 0 1
## concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,] 0 0 0 0.7414877 0 0
## [2,] 0 0 0 -0.4540269 0 0
## [3,] 0 0 0 0.5422353 0 0
## [4,] 0 0 0 0.1437304 0 0
## [5,] 0 0 0 0.1437304 0 0
## [6,] 0 0 0 1.1399926 1 0
## mean_cpss mean_epsd male gest_age_w
## [1,] 0.03508979 -0.95840046 0 0.5959769
## [2,] 0.42874413 -1.31067596 0 -2.2254033
## [3,] 1.21605281 0.09842604 1 1.3742887
## [4,] -0.75221889 -1.31067596 1 0.9851328
## [5,] 1.60970715 1.85980354 0 -0.6687797
## [6,] 0.82239847 0.45070154 0 0.6932659summary(W.scaled)## lat lon lat_lon_int ed_no_hs
## Min. :-2.14565 Min. :-2.1021 Min. :-3.0142020 Min. :0.00000
## 1st Qu.:-0.61475 1st Qu.:-0.6902 1st Qu.:-0.4724605 1st Qu.:0.00000
## Median : 0.06549 Median :-0.0679 Median : 0.0003061 Median :0.00000
## Mean : 0.00000 Mean : 0.0000 Mean : 0.0000000 Mean :0.05393
## 3rd Qu.: 0.38409 3rd Qu.: 0.7585 3rd Qu.: 0.6626216 3rd Qu.:0.00000
## Max. : 3.33626 Max. : 4.1076 Max. : 2.3009871 Max. :1.00000
## ed_hs ed_aa ed_4yr low_bmi
## Min. :0.00000 Min. :0.0000 Min. :0.0000 Min. :0.00000
## 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000
## Median :0.00000 Median :0.0000 Median :0.0000 Median :0.00000
## Mean :0.08315 Mean :0.1618 Mean :0.3303 Mean :0.03146
## 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:0.00000
## Max. :1.00000 Max. :1.0000 Max. :1.0000 Max. :1.00000
## ovwt_bmi obese_bmi concep_spring concep_summer
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.2315 Mean :0.1393 Mean :0.2494 Mean :0.2629
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## concep_fall concep_2010 concep_2011 concep_2012
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.2584 Mean :0.1573 Mean :0.2876 Mean :0.2966
## 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## concep_2013 maternal_age any_smoker smokeSH
## Min. :0.0000 Min. :-2.8451 Min. :0.00000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:-0.6533 1st Qu.:0.00000 1st Qu.:0.000
## Median :0.0000 Median : 0.1437 Median :0.00000 Median :0.000
## Mean :0.2584 Mean : 0.0000 Mean :0.06966 Mean :0.182
## 3rd Qu.:1.0000 3rd Qu.: 0.7415 3rd Qu.:0.00000 3rd Qu.:0.000
## Max. :1.0000 Max. : 2.7340 Max. :1.00000 Max. :1.000
## mean_cpss mean_epsd male gest_age_w
## Min. :-4.68876 Min. :-1.3107 Min. :0.0000 Min. :-6.8953
## 1st Qu.:-0.62100 1st Qu.:-0.7823 1st Qu.:0.0000 1st Qu.:-0.4742
## Median : 0.03509 Median :-0.1364 Median :1.0000 Median : 0.1095
## Mean : 0.00000 Mean : 0.0000 Mean :0.5124 Mean : 0.0000
## 3rd Qu.: 0.69118 3rd Qu.: 0.4507 3rd Qu.:1.0000 3rd Qu.: 0.5960
## Max. : 2.98750 Max. : 3.9735 Max. :1.0000 Max. : 1.8607Variance and histograms for the scaled covariates
var(W.scaled)## lat lon lat_lon_int ed_no_hs
## lat 1.000000000 -0.276115615 -0.928356863 -0.0101130332
## lon -0.276115615 1.000000000 0.613573495 0.0262079705
## lat_lon_int -0.928356863 0.613573495 1.000000000 0.0184474549
## ed_no_hs -0.010113033 0.026207970 0.018447455 0.0511387792
## ed_hs -0.016953107 0.027192891 0.024434547 -0.0044943820
## ed_aa -0.020229967 0.076553174 0.046240217 -0.0087458245
## ed_4yr 0.015291929 -0.006510708 -0.015091570 -0.0178560583
## low_bmi -0.005196646 0.003764983 0.005725894 -0.0017005770
## ovwt_bmi 0.016939252 -0.007162408 -0.016707589 -0.0080068833
## obese_bmi 0.019720120 0.026026302 -0.006128656 0.0059823869
## concep_spring 0.042294895 -0.001716481 -0.035419198 0.0067871242
## concep_summer -0.039711819 0.018991239 0.039990266 -0.0074552080
## concep_fall 0.005023840 -0.001305642 -0.004645539 -0.0004555117
## concep_2010 0.002951929 -0.003179720 -0.003684401 0.0050106286
## concep_2011 -0.044325781 0.037270498 0.050823044 -0.0020346189
## concep_2012 -0.007398114 -0.012020792 0.001446144 0.0019840065
## concep_2013 0.048771966 -0.022069986 -0.048584788 -0.0049600162
## maternal_age 0.109210499 -0.272870082 -0.195251338 -0.0909594732
## any_smoker -0.010940646 0.030990243 0.020970244 0.0232614637
## smokeSH -0.043143276 0.060472659 0.058815490 0.0352059925
## mean_cpss -0.027134738 -0.052301539 0.002117103 -0.0204162448
## mean_epsd -0.046036525 -0.011368895 0.033428064 0.0523961815
## male 0.027341149 -0.032250065 -0.034932167 -0.0029203361
## gest_age_w -0.016388845 -0.005364562 0.011370938 -0.0017485228
## ed_hs ed_aa ed_4yr low_bmi
## lat -0.0169531065 -0.0202299672 0.01529192857 -0.0051966462
## lon 0.0271928911 0.0765531735 -0.00651070784 0.0037649829
## lat_lon_int 0.0244345472 0.0462402175 -0.01509157026 0.0057258937
## ed_no_hs -0.0044943820 -0.0087458245 -0.01785605831 -0.0017005770
## ed_hs 0.0764044944 -0.0134831461 -0.02752808989 0.0018827817
## ed_aa -0.0134831461 0.1359246887 -0.05356817492 0.0016550258
## ed_4yr -0.0275280899 -0.0535681749 0.22171272396 -0.0014070250
## low_bmi 0.0018827817 0.0016550258 -0.00140702500 0.0305395283
## ovwt_bmi -0.0057748760 0.0210243952 0.01120558761 -0.0072983095
## obese_bmi 0.0199210446 0.0089381516 -0.01234436684 -0.0043931572
## concep_spring -0.0005162466 0.0023433546 -0.00150318858 -0.0078651685
## concep_summer -0.0016398421 -0.0088521105 0.00529405810 0.0007186962
## concep_fall 0.0054914465 0.0008857172 0.00002530621 0.0098694200
## concep_2010 0.0116661605 0.0082751291 -0.00703512501 0.0017967406
## concep_2011 -0.0014475149 0.0006529001 0.01963255390 0.0021915174
## concep_2012 -0.0044488309 -0.0075614941 -0.00811823059 -0.0071009211
## concep_2013 -0.0057698148 -0.0013665351 -0.00447919830 0.0031126632
## maternal_age -0.0759807484 -0.0511876462 0.02873821574 -0.0035457615
## any_smoker 0.0099605223 0.0022168236 -0.01630731855 -0.0021965786
## smokeSH 0.0253720012 0.0177801397 -0.02873266525 -0.0012349428
## mean_cpss -0.0384509319 0.0222402682 0.01516400036 -0.0008145512
## mean_epsd 0.0080699343 0.0319614805 -0.02810911729 0.0027068171
## male -0.0021560887 -0.0155177650 0.00604312177 -0.0003897156
## gest_age_w -0.0173857629 -0.0026161368 0.00449169959 0.0047684300
## ovwt_bmi obese_bmi concep_spring concep_summer
## lat 0.016939252 0.0197201196 0.0422948947 -0.0397118186
## lon -0.007162408 0.0260263016 -0.0017164811 0.0189912393
## lat_lon_int -0.016707589 -0.0061286565 -0.0354191979 0.0399902664
## ed_no_hs -0.008006883 0.0059823869 0.0067871242 -0.0074552080
## ed_hs -0.005774876 0.0199210446 -0.0005162466 -0.0016398421
## ed_aa 0.021024395 0.0089381516 0.0023433546 -0.0088521105
## ed_4yr 0.011205588 -0.0123443668 -0.0015031886 0.0052940581
## low_bmi -0.007298310 -0.0043931572 -0.0078651685 0.0007186962
## ovwt_bmi 0.178287276 -0.0323210851 0.0142069035 0.0043222998
## obese_bmi -0.032321085 0.1201842292 0.0012045754 0.0015740460
## concep_spring 0.014206904 0.0012045754 0.1876404494 -0.0657303371
## concep_summer 0.004322300 0.0015740460 -0.0657303371 0.1942301852
## concep_fall -0.001391841 -0.0090596214 -0.0646067416 -0.0680989979
## concep_2010 0.001796741 -0.0084522725 -0.0235600769 -0.0099200324
## concep_2011 -0.003664338 0.0161402976 -0.0065947970 0.0075361879
## concep_2012 -0.005749570 -0.0008806559 -0.0065897358 0.0164287883
## concep_2013 0.007617168 -0.0068073692 0.0367446098 -0.0140449438
## maternal_age 0.037381766 -0.0019191081 -0.0107391395 0.0118464337
## any_smoker -0.007151534 0.0082903128 0.0006022877 -0.0025913554
## smokeSH -0.006189898 0.0173752404 -0.0117218342 -0.0006680838
## mean_cpss 0.015971910 -0.0036706272 -0.0079253536 0.0051091252
## mean_epsd 0.010535162 0.0280256157 -0.0226015810 -0.0051387625
## male -0.003993319 -0.0062303877 0.0070452475 0.0046259743
## gest_age_w -0.060704419 -0.0125331320 -0.0199467506 0.0117718770
## concep_fall concep_2010 concep_2011 concep_2012
## lat 0.00502384034 0.002951929 -0.0443257810 -0.0073981137
## lon -0.00130564175 -0.003179720 0.0372704984 -0.0120207920
## lat_lon_int -0.00464553856 -0.003684401 0.0508230437 0.0014461445
## ed_no_hs -0.00045551169 0.005010629 -0.0020346189 0.0019840065
## ed_hs 0.00549144650 0.011666161 -0.0014475149 -0.0044488309
## ed_aa 0.00088571718 0.008275129 0.0006529001 -0.0075614941
## ed_4yr 0.00002530621 -0.007035125 0.0196325539 -0.0081182306
## low_bmi 0.00986941998 0.001796741 0.0021915174 -0.0071009211
## ovwt_bmi -0.00139184128 0.001796741 -0.0036643385 -0.0057495698
## obese_bmi -0.00905962142 -0.008452272 0.0161402976 -0.0008806559
## concep_spring -0.06460674157 -0.023560077 -0.0065947970 -0.0065897358
## concep_summer -0.06809899787 -0.009920032 0.0075361879 0.0164287883
## concep_fall 0.19207409657 0.035833586 -0.0136906569 -0.0070098188
## concep_2010 0.03583358640 0.132857577 -0.0453487195 -0.0467658670
## concep_2011 -0.01369065695 -0.045348720 0.2053649155 -0.0855147282
## concep_2012 -0.00700981881 -0.046765867 -0.0855147282 0.2091102338
## concep_2013 -0.01513311064 -0.040742990 -0.0745014678 -0.0768296386
## maternal_age -0.02021467293 -0.045103579 -0.0182501839 0.0175997242
## any_smoker -0.00452981071 0.007035125 0.0001872659 -0.0094493370
## smokeSH -0.00210041502 0.009591052 0.0060836117 -0.0135742484
## mean_cpss -0.02460256616 0.008339769 0.0065695393 -0.0157228628
## mean_epsd -0.00756565630 -0.003656536 0.0347223805 -0.0348724455
## male -0.00883186557 -0.008705335 -0.0080676182 -0.0126834700
## gest_age_w 0.02968451108 0.010914111 0.0166767027 -0.0384310645
## concep_2013 maternal_age any_smoker smokeSH
## lat 0.048771966 0.109210499 -0.0109406462 -0.0431432763
## lon -0.022069986 -0.272870082 0.0309902425 0.0604726586
## lat_lon_int -0.048584788 -0.195251338 0.0209702437 0.0588154897
## ed_no_hs -0.004960016 -0.090959473 0.0232614637 0.0352059925
## ed_hs -0.005769815 -0.075980748 0.0099605223 0.0253720012
## ed_aa -0.001366535 -0.051187646 0.0022168236 0.0177801397
## ed_4yr -0.004479198 0.028738216 -0.0163073186 -0.0287326652
## low_bmi 0.003112663 -0.003545762 -0.0021965786 -0.0012349428
## ovwt_bmi 0.007617168 0.037381766 -0.0071515336 -0.0061898978
## obese_bmi -0.006807369 -0.001919108 0.0082903128 0.0173752404
## concep_spring 0.036744610 -0.010739140 0.0006022877 -0.0117218342
## concep_summer -0.014044944 0.011846434 -0.0025913554 -0.0006680838
## concep_fall -0.015133111 -0.020214673 -0.0045298107 -0.0021004150
## concep_2010 -0.040742990 -0.045103579 0.0070351250 0.0095910517
## concep_2011 -0.074501468 -0.018250184 0.0001872659 0.0060836117
## concep_2012 -0.076829639 0.017599724 -0.0094493370 -0.0135742484
## concep_2013 0.192074097 0.045754039 0.0022269460 -0.0021004150
## maternal_age 0.045754039 1.000000000 -0.0649088156 -0.1555294446
## any_smoker 0.002226946 -0.064908816 0.0649559672 0.0458497824
## smokeSH -0.002100415 -0.155529445 0.0458497824 0.1492256301
## mean_cpss 0.000813555 0.109685178 0.0088039929 -0.0046810956
## mean_epsd 0.003806601 -0.112036096 0.0487907570 0.1019256746
## male 0.029456423 -0.014599542 0.0115244458 0.0056281000
## gest_age_w 0.010840251 0.017621395 -0.0096629152 -0.0275666860
## mean_cpss mean_epsd male gest_age_w
## lat -0.0271347383 -0.046036525 0.0273411490 -0.016388845
## lon -0.0523015387 -0.011368895 -0.0322500653 -0.005364562
## lat_lon_int 0.0021171030 0.033428064 -0.0349321671 0.011370938
## ed_no_hs -0.0204162448 0.052396181 -0.0029203361 -0.001748523
## ed_hs -0.0384509319 0.008069934 -0.0021560887 -0.017385763
## ed_aa 0.0222402682 0.031961481 -0.0155177650 -0.002616137
## ed_4yr 0.0151640004 -0.028109117 0.0060431218 0.004491700
## low_bmi -0.0008145512 0.002706817 -0.0003897156 0.004768430
## ovwt_bmi 0.0159719102 0.010535162 -0.0039933192 -0.060704419
## obese_bmi -0.0036706272 0.028025616 -0.0062303877 -0.012533132
## concep_spring -0.0079253536 -0.022601581 0.0070452475 -0.019946751
## concep_summer 0.0051091252 -0.005138763 0.0046259743 0.011771877
## concep_fall -0.0246025662 -0.007565656 -0.0088318656 0.029684511
## concep_2010 0.0083397685 -0.003656536 -0.0087053345 0.010914111
## concep_2011 0.0065695393 0.034722380 -0.0080676182 0.016676703
## concep_2012 -0.0157228628 -0.034872446 -0.0126834700 -0.038431064
## concep_2013 0.0008135550 0.003806601 0.0294564227 0.010840251
## maternal_age 0.1096851777 -0.112036096 -0.0145995420 0.017621395
## any_smoker 0.0088039929 0.048790757 0.0115244458 -0.009662915
## smokeSH -0.0046810956 0.101925675 0.0056281000 -0.027566686
## mean_cpss 1.0000000000 0.524941092 0.0121083543 -0.032877684
## mean_epsd 0.5249410917 1.000000000 -0.0060537137 -0.078848395
## male 0.0121083543 -0.006053714 0.2504099605 -0.026800015
## gest_age_w -0.0328776840 -0.078848395 -0.0268000147 1.000000000ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.3 Response data: birth weight (in grams)
Y <- select(hs_data2, birth_weight) %>%
as.matrix()
head(Y)## birth_weight
## [1,] 3505
## [2,] 2695
## [3,] 3080
## [4,] 3440
## [5,] 3394
## [6,] 3060Distribution of birth weight and scaled birth weight
hist(Y, breaks = 20)
hist(scale(Y), breaks = 20)
Dropping gest_age_w from the covariates
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male" "gest_age_w"W.scaled2 <- W.scaled[,-c(ncol(W.scaled))]
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"2 RIDGE regression
To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.
set.seed(123)
library(glmnet)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loaded glmnet 4.0-2lambda_seq <- 10^seq(4, -4, by = -.05)
#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
standardize = T, standardize.response = T)
plot(ridge_cv)
best_lambda <- ridge_cv$lambda.min
best_lambda## [1] 1412.538#' Fit the model using the best_lambda
bw_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
standardize = T, standardize.response = T)
summary(bw_ridge)## Length Class Mode
## a0 1 -none- numeric
## beta 21 dgCMatrix S4
## df 1 -none- numeric
## dim 2 -none- numeric
## lambda 1 -none- numeric
## dev.ratio 1 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numericRidge regression coefficients
coef(bw_ridge)## 22 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 3527.88072827513
## mean_pm 12.92287834239
## mean_o3 -3.56744503831
## mean_temp -1.62693356046
## pct_tree_cover -0.36388972149
## pct_impervious -0.38915239035
## mean_aadt_intensity -0.00064476176
## dist_m_tri -0.00015504654
## dist_m_npl 0.00094355434
## dist_m_waste_site 0.00386069844
## dist_m_major_emit -0.00022887802
## dist_m_cafo -0.00001289458
## dist_m_mine_well -0.00217878564
## cvd_rate_adj 0.01460307637
## res_rate_adj -0.04961523133
## violent_crime_rate -0.34399332077
## property_crime_rate -0.11006094025
## pct_less_hs -0.83661364882
## pct_unemp -1.82571596409
## pct_limited_eng -0.03277560580
## pct_hh_pov -1.01466481202
## pct_poc 0.06420714355Ridge regression predictions
ridge_pred <- predict(bw_ridge, newx = X)
plot(Y, ridge_pred)
actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))The R2 value for this model is 0.02. Based on these results, it doesn’t look like there’s much here.
3 Nonparametric Bayesian Shrinkage (NPB): Birth weight
3.1 Finding the NPB priors
3.1.1 Vignette Priors
set.seed(123)
priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1)
fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 0.064024028 2.543619 -0.87540148 0.0000000 0.052
## [2,] -0.276967213 6.076312 -2.31592821 0.0000000 0.062
## [3,] -0.054355789 2.716440 -1.91194054 0.0000000 0.048
## [4,] -0.116003999 1.708604 -2.45222406 0.0000000 0.056
## [5,] -0.086183823 1.136087 -0.65445017 0.0000000 0.048
## [6,] -0.018782823 2.355395 -1.45280779 0.0000000 0.048
## [7,] -0.238014150 2.103096 -3.20257683 0.0000000 0.052
## [8,] -0.021394839 1.345509 -1.13858590 0.0000000 0.054
## [9,] 0.007711504 2.304692 0.00000000 0.0000000 0.034
## [10,] -0.259099107 2.697696 -4.80388637 0.4523284 0.076
## [11,] -0.005218549 5.063448 -0.83486231 0.0000000 0.050
## [12,] -0.217555692 2.274577 -1.45726486 0.0000000 0.048
## [13,] -0.031911453 1.072786 -0.08358356 0.0000000 0.044
## [14,] -0.118847360 1.209560 -2.23979385 0.0000000 0.052
## [15,] -0.299300660 2.324544 -4.50741969 0.0000000 0.048
## [16,] -0.228573895 1.718744 -3.48895890 0.0000000 0.050
## [17,] -0.375037028 3.282522 -4.40274535 0.0000000 0.056
## [18,] -0.393435283 4.048178 -2.72973606 0.0000000 0.062
## [19,] -0.085530085 1.794808 0.00000000 0.0000000 0.038
## [20,] -0.138509647 1.384727 -1.45726486 0.0000000 0.052
## [21,] -0.046301207 1.926945 -0.08358356 0.0000000 0.042plot(fit.npb.1$beta[,1], type = "l")
plot(fit.npb.1$beta[,2], type = "l")
plot(fit.npb.1$beta[,13], type = "l")
3.1.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10
priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 10, sig2inv.mu1 = 10)
fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 1.7957383 11.481073 -11.64536 33.690294 0.326
## [2,] -0.9188404 8.737149 -19.01183 15.001499 0.388
## [3,] -0.4102169 7.508868 -16.80982 12.899458 0.314
## [4,] -0.5897400 6.442544 -17.72104 12.060223 0.294
## [5,] -1.2417945 7.058161 -17.06653 11.333702 0.348
## [6,] -1.0077776 5.718843 -15.90191 7.650775 0.322
## [7,] -1.9350059 7.197606 -19.62186 7.423318 0.362
## [8,] -0.6090866 6.571676 -15.74636 11.658495 0.312
## [9,] 1.7331228 10.603277 -11.82677 33.043033 0.314
## [10,] -1.5093281 6.785545 -17.28844 8.687978 0.346
## [11,] 0.1315822 16.683248 -20.37527 34.019055 0.432
## [12,] -1.7224704 8.093652 -19.98394 10.884684 0.390
## [13,] -1.2666731 7.309715 -18.11823 10.967504 0.342
## [14,] -0.4624574 7.833527 -17.43480 13.485397 0.338
## [15,] -1.7580037 7.104701 -19.01183 7.188367 0.328
## [16,] -1.9091204 7.134364 -19.41213 6.902233 0.346
## [17,] -3.7007804 11.623333 -35.87865 6.332795 0.370
## [18,] -3.2754502 9.445498 -29.31882 4.876851 0.388
## [19,] -0.5847352 6.535276 -16.89740 11.250882 0.316
## [20,] -2.1849981 7.766824 -18.65988 4.291485 0.320
## [21,] -0.4432643 7.217683 -14.03179 13.485397 0.354plot(fit.npb.24$beta[,1], type = "l")
plot(fit.npb.24$beta[,2], type = "l")
plot(fit.npb.24$beta[,13], type = "l")
3.2 Run the NPB model with temperaure and ozone
Below I’ve used the set of priors labeled “24” and set scaleY = T
The priors are as follows: r priors.npb.24
Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "ed_no_hs"
## [5] "ed_hs" "ed_aa" "ed_4yr" "low_bmi"
## [9] "ovwt_bmi" "obese_bmi" "concep_spring" "concep_summer"
## [13] "concep_fall" "concep_2010" "concep_2011" "concep_2012"
## [17] "concep_2013" "maternal_age" "any_smoker" "smokeSH"
## [21] "mean_cpss" "mean_epsd" "male"# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Birth_Weight_v4b.2.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4b.2.rdata"))
npb.sum2 <- summary(fit.npb2)3.2.1 First, main effect regression coefficients with PIPs
rownames(npb.sum2$main.effects) <- colnames(X.scaled)
npb.sum2$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm 1.268902333 10.417098 -14.05244 27.819013 0.3240
## mean_o3 -1.259539645 11.458852 -23.36137 17.622385 0.3464
## mean_temp -1.069097141 10.241296 -21.98910 14.468908 0.3304
## pct_tree_cover -0.078352795 7.963849 -15.27524 17.515597 0.3068
## pct_impervious -1.295749287 7.559532 -20.39060 10.947726 0.3116
## mean_aadt_intensity -0.948901315 6.696318 -18.73738 11.902765 0.3044
## dist_m_tri -2.261932420 8.954852 -25.95040 9.679603 0.3544
## dist_m_npl -0.001456136 8.068803 -14.79201 20.708611 0.2936
## dist_m_waste_site 1.603415112 9.787915 -12.12510 31.900579 0.3300
## dist_m_major_emit -1.014542477 6.483008 -17.82933 10.168955 0.3108
## dist_m_cafo -0.345983398 17.922511 -21.95897 24.847532 0.3464
## dist_m_mine_well -1.774967871 8.530910 -24.07593 12.191663 0.3532
## cvd_rate_adj -0.962495984 7.750207 -19.08625 13.423337 0.3212
## res_rate_adj -0.795277915 7.539974 -17.83655 12.090056 0.3024
## violent_crime_rate -1.074732152 6.787745 -18.71497 11.463321 0.3112
## property_crime_rate -1.855522242 7.623709 -22.20365 9.666131 0.3152
## pct_less_hs -2.801052168 10.423547 -30.58982 6.879719 0.3340
## pct_unemp -2.883291385 9.697163 -29.26122 6.658777 0.3420
## pct_limited_eng -0.723654955 6.642270 -16.31429 12.382738 0.2992
## pct_hh_pov -2.392325916 9.287666 -27.35829 8.044338 0.3284
## pct_poc -0.587480004 6.912553 -16.51112 12.312259 0.28683.2.2 Next, posterior means and CIs for covariates
rownames(npb.sum2$covariates)[2:nrow(npb.sum2$covariates)] <- colnames(W.scaled2)
npb.sum2$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3228.326209 222.67637 2788.9548067 3650.08120
## lat 4.285981 300.13991 -571.0068298 593.98717
## lon 50.148586 144.37522 -228.9600827 331.44758
## lat_lon_int 19.524814 364.47146 -673.2609210 729.46694
## ed_no_hs 60.840450 135.63121 -205.4633140 328.89200
## ed_hs -15.853723 102.12111 -212.4909849 183.00463
## ed_aa 59.835434 74.54864 -86.7330318 206.40529
## ed_4yr 33.932334 55.75500 -75.6201494 146.45910
## low_bmi -161.622737 130.37224 -412.3212422 91.92116
## ovwt_bmi -34.149893 56.44149 -143.9161031 78.57550
## obese_bmi 86.820801 70.48844 -49.8578539 222.12717
## concep_spring 33.644906 67.99972 -98.3356717 169.65375
## concep_summer 77.726233 70.02767 -64.7122807 218.37422
## concep_fall 134.534361 79.13387 -12.3059481 310.35421
## concep_2010 -10.629032 222.55011 -432.7755354 418.80507
## concep_2011 1.765741 219.80058 -420.1884377 428.45655
## concep_2012 -111.174256 220.38802 -530.8592887 306.32967
## concep_2013 22.618586 222.23168 -406.2976931 451.05180
## maternal_age 58.792403 29.52098 0.9624005 117.29717
## any_smoker -140.608145 102.38497 -345.5139953 60.99820
## smokeSH -88.396910 75.02847 -234.3954605 56.14670
## mean_cpss 3.710801 28.74716 -51.4516737 59.44288
## mean_epsd -20.000502 29.03108 -76.3663364 37.61056
## male 110.128534 45.68797 20.1138369 197.478763.2.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum2$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.00769875041 0.4113312 0.00000 0.0000 0.0040
## [2,] 0.00059795405 0.4648037 0.00000 0.0000 0.0056
## [3,] -0.00116448464 0.2891330 0.00000 0.0000 0.0020
## [4,] -0.03922382107 1.0130056 0.00000 0.0000 0.0056
## [5,] 0.00695433562 0.4319350 0.00000 0.0000 0.0024
## [6,] -0.00377542156 0.2844888 0.00000 0.0000 0.0032
## [7,] -0.00707303850 0.5513934 0.00000 0.0000 0.0052
## [8,] -0.00220359051 0.3182526 0.00000 0.0000 0.0032
## [9,] -0.03448487267 1.3064791 0.00000 0.0000 0.0020
## [10,] -0.07516766149 1.5012843 0.00000 0.0000 0.0064
## [11,] -0.00052198052 0.3345314 0.00000 0.0000 0.0036
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## [581,] -0.00581490046 0.4423204 0.00000 0.0000 0.0040
## [582,] -0.02606931502 1.7931706 0.00000 0.0000 0.0048
## [583,] -0.02702163895 0.6713354 0.00000 0.0000 0.0052
## [584,] -0.01842901049 0.7218367 0.00000 0.0000 0.0040
## [585,] -0.15872977084 3.2080013 0.00000 0.0000 0.0060
## [586,] 0.08389018469 3.6039164 0.00000 0.0000 0.0016
## [587,] 0.00038806967 0.3672994 0.00000 0.0000 0.0032
## [588,] -0.25795439273 5.1353457 0.00000 0.0000 0.0068
## [589,] -0.48608457583 7.6498739 0.00000 0.0000 0.0088
## [590,] -0.00802561687 0.4227186 0.00000 0.0000 0.0044
## [591,] -0.04024175896 1.4416101 0.00000 0.0000 0.0020
## [592,] 0.05991073884 2.9831163 0.00000 0.0000 0.0040
## [593,] -0.09934179787 2.1042539 0.00000 0.0000 0.0044
## [594,] -0.01221089429 0.6211732 0.00000 0.0000 0.0044
## [595,] -0.09728793260 2.8910277 0.00000 0.0000 0.0056
## [596,] -0.02357146205 0.5400814 0.00000 0.0000 0.0028
## [597,] -0.03769460606 1.8298453 0.00000 0.0000 0.0060
## [598,] 0.03722744017 2.5259169 0.00000 0.0000 0.0052
## [599,] -0.01403809899 0.6955268 0.00000 0.0000 0.0028
## [600,] -0.00279151472 0.3384934 0.00000 0.0000 0.0036
## [601,] -0.34230966147 4.7906850 0.00000 0.0000 0.0100
## [602,] -0.01512593870 0.5582302 0.00000 0.0000 0.0052
## [603,] -0.02037469408 0.8883290 0.00000 0.0000 0.0056
## [604,] -0.00939840080 0.4845240 0.00000 0.0000 0.0048
## [605,] 0.00549360618 0.4381474 0.00000 0.0000 0.0020
## [606,] 0.40729559966 8.7120614 0.00000 0.0000 0.0048
## [607,] -0.03603302394 1.3762765 0.00000 0.0000 0.0052
## [608,] -1.63058258413 13.3994865 0.00000 0.0000 0.0220
## [609,] -0.02700141747 1.3612281 0.00000 0.0000 0.0044
## [610,] -0.04868388185 1.4625255 0.00000 0.0000 0.0028
## [611,] -0.05502920798 1.3940249 0.00000 0.0000 0.0068
## [612,] -0.05408136219 1.7040516 0.00000 0.0000 0.0036
## [613,] -0.02740444379 0.7505288 0.00000 0.0000 0.0040
## [614,] -0.00561482463 1.0083766 0.00000 0.0000 0.0056
## [615,] -0.02004677999 1.4795313 0.00000 0.0000 0.0024
## [616,] -0.12913689552 3.4252177 0.00000 0.0000 0.0056
## [617,] 0.02325429239 1.1302185 0.00000 0.0000 0.0048
## [618,] -0.12025295677 3.0700794 0.00000 0.0000 0.0040
## [619,] -0.05009662903 1.5926231 0.00000 0.0000 0.0028
## [620,] -0.09141923437 3.1969494 0.00000 0.0000 0.0048
## [621,] -0.06350196597 1.9593231 0.00000 0.0000 0.0044
## [622,] 0.00839579421 0.3080303 0.00000 0.0000 0.0032
## [623,] 0.00084266129 0.6312353 0.00000 0.0000 0.0052
## [624,] -0.36342270793 5.5362577 0.00000 0.0000 0.0100
## [625,] -0.08043972691 1.6784085 0.00000 0.0000 0.0068
## [626,] -0.02184861268 1.2489367 0.00000 0.0000 0.0040
## [627,] 0.01715453739 0.8804932 0.00000 0.0000 0.0032
## [628,] -0.00994879841 1.1322588 0.00000 0.0000 0.0028
## [629,] -0.01328127933 1.0050553 0.00000 0.0000 0.0036
## [630,] -0.00927151182 0.7166267 0.00000 0.0000 0.0028
## [631,] -0.00738518217 1.6527724 0.00000 0.0000 0.0068
## [632,] -0.00106871768 0.1265114 0.00000 0.0000 0.0024
## [633,] -0.02301030672 1.2726529 0.00000 0.0000 0.0080
## [634,] -0.04930495560 1.3778623 0.00000 0.0000 0.0052
## [635,] -0.05782478230 1.4320141 0.00000 0.0000 0.0044
## [636,] -0.00058011961 1.0826969 0.00000 0.0000 0.0020
## [637,] 0.05187755550 2.4821179 0.00000 0.0000 0.0040
## [638,] -0.01120569630 0.5420322 0.00000 0.0000 0.0036
## [639,] -0.04786985142 1.2028871 0.00000 0.0000 0.0064
## [640,] 0.01378020588 1.1902183 0.00000 0.0000 0.0044
## [641,] -0.00827690405 0.5285552 0.00000 0.0000 0.0040
## [642,] -0.02179855209 0.9380286 0.00000 0.0000 0.0040
## [643,] -0.02636909075 0.9334187 0.00000 0.0000 0.0060
## [644,] -0.00489087889 1.0321457 0.00000 0.0000 0.0040
## [645,] -0.00718481339 0.4985295 0.00000 0.0000 0.0020
## [646,] 0.01391585731 0.5376600 0.00000 0.0000 0.0040
## [647,] -0.02144296210 0.6852352 0.00000 0.0000 0.0052
## [648,] -0.02107174174 0.7242061 0.00000 0.0000 0.0036
## [649,] -0.00635279710 0.4149004 0.00000 0.0000 0.0032
## [650,] 0.01076489108 0.7802904 0.00000 0.0000 0.0036
## [651,] -0.03712005318 1.3418039 0.00000 0.0000 0.0036
## [652,] -0.00764874157 0.5726982 0.00000 0.0000 0.0036
## [653,] -0.04494232280 1.7145491 0.00000 0.0000 0.0024
## [654,] -0.01654217210 0.9977905 0.00000 0.0000 0.0048
## [655,] -0.16076937682 4.3320576 0.00000 0.0000 0.0064
## [656,] -0.05190527333 1.2671586 0.00000 0.0000 0.0036
## [657,] -0.02551092536 0.9270217 0.00000 0.0000 0.0032
## [658,] -0.06570075369 2.2272467 0.00000 0.0000 0.0032
## [659,] -0.00502617813 0.3052554 0.00000 0.0000 0.0012
## [660,] 0.01032296252 0.4043590 0.00000 0.0000 0.0016
## [661,] -0.06642314875 2.5078787 0.00000 0.0000 0.0060
## [662,] -0.03356336954 1.0062210 0.00000 0.0000 0.0052
## [663,] 0.05625419349 2.0628764 0.00000 0.0000 0.0040
## [664,] -0.01245983636 0.6697871 0.00000 0.0000 0.0044
## [665,] -0.00845625132 0.4204365 0.00000 0.0000 0.0032
## [666,] 0.01168857255 2.1705254 0.00000 0.0000 0.0048
## [667,] -0.03142183555 1.5140836 0.00000 0.0000 0.0028
## [668,] -0.01995430455 0.5408620 0.00000 0.0000 0.0024
## [669,] 0.00433839071 0.7119034 0.00000 0.0000 0.0068
## [670,] -0.26667541472 4.3068049 0.00000 0.0000 0.0084
## [671,] -0.02803173467 1.4835196 0.00000 0.0000 0.0048
## [672,] 0.00101337570 0.4256440 0.00000 0.0000 0.0040
## [673,] 0.02990345868 1.0160220 0.00000 0.0000 0.0040
## [674,] -0.05968635033 1.4501770 0.00000 0.0000 0.0052
## [675,] -0.00495262520 0.1776880 0.00000 0.0000 0.0024
## [676,] -0.01569551812 1.4021773 0.00000 0.0000 0.0048
## [677,] -0.06826071069 2.1210282 0.00000 0.0000 0.0056
## [678,] -0.09455256251 2.6717979 0.00000 0.0000 0.0064
## [679,] 0.07258164237 2.3456410 0.00000 0.0000 0.0040
## [680,] -0.06158137459 1.7814387 0.00000 0.0000 0.0040
## [681,] -0.03223576531 2.0473225 0.00000 0.0000 0.0040
## [682,] 0.04720113571 2.4969594 0.00000 0.0000 0.0048
## [683,] 0.01687818378 0.4608714 0.00000 0.0000 0.0032
## [684,] -0.05212446226 2.4020504 0.00000 0.0000 0.0040
## [685,] 0.00257794645 0.5989752 0.00000 0.0000 0.0032
## [686,] 0.22471634305 5.5725886 0.00000 0.0000 0.0084
## [687,] -0.05690365650 2.0806055 0.00000 0.0000 0.0032
## [688,] -0.00441251512 0.4018209 0.00000 0.0000 0.0032
## [689,] -0.05993846525 2.1765355 0.00000 0.0000 0.0040
## [690,] -0.01441780180 0.5942107 0.00000 0.0000 0.0020
## [691,] -0.01958745926 0.7149677 0.00000 0.0000 0.0028
## [692,] 0.00628593521 0.3077307 0.00000 0.0000 0.0016
## [693,] -0.06516600345 1.6650428 0.00000 0.0000 0.00523.2.4 Predict fitted values for each individual
pred.npb2 <- predict(fit.npb2)
fittedvals2 <- pred.npb2$fitted.vals3.2.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals2, Y)
abline(a = 0, b = 1, col = "red")
4 Linear models for each predictor
4.1 Screening the exposures
Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.
The standard deviation of the mean_o3 variable is 2.98 ppb
lm_results <- data.frame()
for(i in 1:length(colnames(X.scaled))) {
lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
names(lm_df)[2] <- colnames(X.scaled)[i]
ad_lm <- lm(birth_weight ~ ., data = lm_df)
temp <- data.frame(exp = colnames(X.scaled)[i],
beta = summary(ad_lm)$coefficients[2,1],
beta.se = summary(ad_lm)$coefficients[2,2],
p.value = summary(ad_lm)$coefficients[2,4])
temp$lcl <- temp$beta - 1.96*temp$beta.se
temp$ucl <- temp$beta + 1.96*temp$beta.se
lm_results <- bind_rows(lm_results, temp)
rm(temp)
}
lm_resultswrite_csv(lm_results, here::here("Results", "LM_Effects_Birth_Weight_v4b.csv"))5 Linear model with the ozone and temperature predictors
The standard deviation of the mean_o3 variable is 2.98 ppb The standard deviation of the mean_temp variable is 4.39 degrees F
lm_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(lm_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"#names(lm_df)[2] <- "mean_o3"
head(lm_df)bw_lm <- lm(birth_weight ~ mean_o3 + mean_temp + mean_o3*mean_temp +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = lm_df)
summary(bw_lm)##
## Call:
## lm(formula = birth_weight ~ mean_o3 + mean_temp + mean_o3 * mean_temp +
## lat + lon + lat_lon_int + ed_no_hs + ed_hs + ed_aa + ed_4yr +
## low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer +
## concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 +
## maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd +
## male, data = lm_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2098.72 -304.96 12.59 329.55 1142.03
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3327.6603 87.5116 38.025 < 0.0000000000000002 ***
## mean_o3 -25.2753 70.7784 -0.357 0.721193
## mean_temp 33.1198 68.7757 0.482 0.630368
## lat 594.1046 24436.0007 0.024 0.980615
## lon -229.7916 11503.6831 -0.020 0.984072
## lat_lon_int 731.6944 29742.5406 0.025 0.980385
## ed_no_hs 63.9484 141.0645 0.453 0.650548
## ed_hs -4.0768 105.0427 -0.039 0.969060
## ed_aa 60.8840 77.1412 0.789 0.430410
## ed_4yr 43.9070 55.4575 0.792 0.428970
## low_bmi -179.1352 130.6846 -1.371 0.171188
## ovwt_bmi -20.3753 56.9547 -0.358 0.720713
## obese_bmi 90.4497 70.8873 1.276 0.202675
## concep_spring -23.4264 81.4981 -0.287 0.773912
## concep_summer 41.0057 109.5242 0.374 0.708297
## concep_fall 130.5375 105.5392 1.237 0.216831
## concep_2010 -64.7424 77.5397 -0.835 0.404217
## concep_2011 -40.8999 66.3215 -0.617 0.537773
## concep_2012 -94.0865 86.3586 -1.089 0.276566
## concep_2013 NA NA NA NA
## maternal_age 58.6162 28.9951 2.022 0.043854 *
## any_smoker -137.0995 104.1625 -1.316 0.188824
## smokeSH -91.4934 74.1925 -1.233 0.218196
## mean_cpss 0.1884 28.0725 0.007 0.994649
## mean_epsd -14.6595 29.2594 -0.501 0.616620
## male 119.2181 45.5898 2.615 0.009244 **
## mean_o3:mean_temp -86.1535 24.5931 -3.503 0.000509 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 466.6 on 419 degrees of freedom
## Multiple R-squared: 0.1121, Adjusted R-squared: 0.05917
## F-statistic: 2.117 on 25 and 419 DF, p-value: 0.001519plot(bw_lm)
6 Try a GAM with the ozone and temperature predictor
The NPB model above indicates that there might be a signal for ozone. None of the other exposures had a PIP > 0.5. Here I’ve got a GAM with a smoothing term for ozone and temperature to see about potential nonlinear effects
The mean and standard deviation of the mean_o3 variable are 47.81 (2.98) ppb The mean and standard deviation of the mean_temp variable is 52.5 (4.39) degrees F
library(mgcv)## Loading required package: nlme##
## Attaching package: 'nlme'## The following object is masked from 'package:dplyr':
##
## collapse## This is mgcv 1.8-34. For overview type 'help("mgcv-package")'.library(tidymv)
gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"#names(gam_df)[2] <- "mean_o3"
head(gam_df)bw_gam <- gam(birth_weight ~ s(mean_o3, mean_temp) +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df, method = "REML")
gam.check(bw_gam)
##
## Method: REML Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-0.001324346,-0.00126227]
## (score 3211.236 & scale 193952.8).
## Hessian positive definite, eigenvalue range [3.665994,209.8084].
## Model rank = 52 / 53
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(mean_o3,mean_temp) 29.0 17.9 1.02 0.6summary(bw_gam)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int +
## ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi +
## obese_bmi + concep_spring + concep_summer + concep_fall +
## concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age +
## any_smoker + smokeSH + mean_cpss + mean_epsd + male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3365.787 92.388 36.431 < 0.0000000000000002 ***
## lat -2496.029 23705.662 -0.105 0.91620
## lon 1221.293 11160.107 0.109 0.91291
## lat_lon_int -3027.331 28853.310 -0.105 0.91649
## ed_no_hs 92.295 135.968 0.679 0.49766
## ed_hs 18.361 101.005 0.182 0.85584
## ed_aa 74.299 74.448 0.998 0.31888
## ed_4yr 44.317 53.212 0.833 0.40543
## low_bmi -231.999 124.833 -1.858 0.06383 .
## ovwt_bmi -5.915 54.924 -0.108 0.91429
## obese_bmi 81.417 68.512 1.188 0.23538
## concep_spring -35.688 86.213 -0.414 0.67913
## concep_summer -175.477 128.764 -1.363 0.17371
## concep_fall -46.658 127.841 -0.365 0.71533
## concep_2010 -82.959 79.747 -1.040 0.29883
## concep_2011 -65.399 67.113 -0.974 0.33041
## concep_2012 -87.596 90.803 -0.965 0.33528
## concep_2013 0.000 0.000 NA NA
## maternal_age 54.777 27.790 1.971 0.04939 *
## any_smoker -128.222 99.068 -1.294 0.19631
## smokeSH -105.556 71.127 -1.484 0.13858
## mean_cpss 3.976 27.151 0.146 0.88365
## mean_epsd -30.141 28.155 -1.071 0.28501
## male 120.075 43.590 2.755 0.00614 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3,mean_temp) 17.9 22.98 2.749 0.000035 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Rank: 52/53
## R-sq.(adj) = 0.162 Deviance explained = 23.7%
## -REML = 3211.2 Scale est. = 1.9395e+05 n = 445save(gam_df, bw_gam, file = here::here("Results", "BW_GAM_v4b.rdata"))library(mgcViz)## Loading required package: qgam## Loading required package: rgl## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2## Registered S3 method overwritten by 'mgcViz':
## method from
## +.gg GGally##
## Attaching package: 'mgcViz'## The following objects are masked from 'package:stats':
##
## qqline, qqnorm, qqplotgam_b <- getViz(bw_gam)
plot(sm(gam_b, 1)) +
l_fitRaster() + l_fitContour() + l_points() +
labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
guides(fill=guide_legend(title="Change in\nbirth weight (g)"))
ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_v4b.jpeg"),
device = "jpeg", width = 5, height = 3, units = "in", dpi = 500) 7 GAM Sensitivity Analysis
The previous GAM suggested a possible nonlinear relationship between ozone and birth weight. However, this might be the influence of abnormally high and low exposures.
Therefore, Ander suggested a sensitivity analysis where we excluded the top and bottom 2.5% of data and just use the middle 95%.
library(mgcv)
gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"head(gam_df)gam_df2 <- gam_df %>%
filter(mean_o3 > -2 & mean_o3 < 2) %>%
filter(mean_temp > -2 & mean_temp < 2)
hist(gam_df2$mean_o3)
hist(gam_df2$mean_temp)
bw_gam2 <- gam(birth_weight ~ s(mean_o3, mean_temp) +
lat + lon + lat_lon_int +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df2, method = "REML")
gam.check(bw_gam2)
##
## Method: REML Optimizer: outer newton
## full convergence after 7 iterations.
## Gradient range [-0.000632231,0.001433747]
## (score 3103.602 & scale 189210.4).
## Hessian positive definite, eigenvalue range [0.4706214,203.5373].
## Model rank = 52 / 53
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(mean_o3,mean_temp) 29.00 7.61 0.99 0.42summary(bw_gam2)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int +
## ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi +
## obese_bmi + concep_spring + concep_summer + concep_fall +
## concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age +
## any_smoker + smokeSH + mean_cpss + mean_epsd + male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3204.53 104.79 30.581 <0.0000000000000002 ***
## lat 10154.91 23417.30 0.434 0.6648
## lon -4744.59 11024.47 -0.430 0.6672
## lat_lon_int 12366.92 28502.69 0.434 0.6646
## ed_no_hs 88.57 133.59 0.663 0.5077
## ed_hs 31.34 99.91 0.314 0.7539
## ed_aa 96.34 73.94 1.303 0.1934
## ed_4yr 54.99 52.66 1.044 0.2970
## low_bmi -216.33 122.61 -1.764 0.0784 .
## ovwt_bmi -29.33 54.34 -0.540 0.5897
## obese_bmi 72.50 67.66 1.071 0.2846
## concep_spring 39.66 82.53 0.481 0.6311
## concep_summer -19.76 117.26 -0.168 0.8663
## concep_fall 69.69 113.39 0.615 0.5392
## concep_2010 48.51 84.78 0.572 0.5676
## concep_2011 54.23 73.19 0.741 0.4592
## concep_2012 0.00 0.00 NA NA
## concep_2013 113.81 85.39 1.333 0.1834
## maternal_age 56.20 27.51 2.043 0.0417 *
## any_smoker -134.60 97.46 -1.381 0.1680
## smokeSH -121.30 70.20 -1.728 0.0848 .
## mean_cpss 11.12 26.89 0.413 0.6795
## mean_epsd -31.43 27.73 -1.133 0.2577
## male 93.79 43.30 2.166 0.0309 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3,mean_temp) 7.611 10.68 0.735 0.723
##
## Rank: 52/53
## R-sq.(adj) = 0.0544 Deviance explained = 11.9%
## -REML = 3103.6 Scale est. = 1.8921e+05 n = 433save(gam_df2, bw_gam2, file = here::here("Results", "BW_GAM_Sensitivity_v4b.rdata"))library(mgcViz)
gam_b2 <- getViz(bw_gam2)
plot(sm(gam_b2, 1)) +
l_fitRaster() + l_fitContour() + l_points() +
labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
guides(fill=guide_legend(title="Change in\nbirth weight (g)"))
ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_Sensitivity_v4b.jpeg"),
device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)